Soft operators are central in the study of the relationship between soft theorems and asymptotic symmetries in flat space-time [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}. These operators live on the celestial sphere \(S^{D-2}\)  and transform as primaries of the Lorentz group \(SO(D-1,1)\) , which acts on the celestial sphere by conformal transformation. In this paper, following [15]}, we continue our study of the properties of the conformal representation with a soft operator as the highest weight state.
